U.S. patent number 5,289,501 [Application Number 07/797,831] was granted by the patent office on 1994-02-22 for coded modulation with unequal error protection for fading channels.
This patent grant is currently assigned to AT&T Bell Laboratories. Invention is credited to Nambirajan Seshadri, Carl-Erik W. Sundberg.
United States Patent |
5,289,501 |
Seshadri , et al. |
February 22, 1994 |
Coded modulation with unequal error protection for fading
channels
Abstract
Information is transmitted in digital form over fading channels
using DPSK coded modulation incorporating multi-level coding in
order to provide unequal error protection for different classes of
data such as generated by CELP or other speech encoders.
Inventors: |
Seshadri; Nambirajan (Chatham,
NJ), Sundberg; Carl-Erik W. (Chatham, NJ) |
Assignee: |
AT&T Bell Laboratories
(Murray Hill, NJ)
|
Family
ID: |
25171911 |
Appl.
No.: |
07/797,831 |
Filed: |
November 26, 1991 |
Current U.S.
Class: |
375/286; 375/254;
375/264; 375/298; 714/758; 714/786 |
Current CPC
Class: |
H03M
13/25 (20130101); H04L 27/186 (20130101); H03M
13/35 (20130101); H04L 2001/0098 (20130101) |
Current International
Class: |
H03M
13/25 (20060101); H04L 27/18 (20060101); H03M
13/35 (20060101); H03M 13/00 (20060101); H04L
1/00 (20060101); H04L 025/49 () |
Field of
Search: |
;375/17,34,39,38,60
;371/37.1,37.7,43,37.8 ;341/94 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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485105 |
|
Oct 1991 |
|
EP |
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485108 |
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Oct 1991 |
|
EP |
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Other References
W F. Schreiber, "Spread-Spectrum Television Broadcasting", SMPTE
Jrn., Aug. 1992, pp. 538-549. .
K. M. Uz et al., "Multiresolution Source & Channel Coding . . .
", Signal Processing of HDTV, III, 1992 Elsevier Science Publisher
pp. 61-69. .
M. Vetterli et al. "Multiresolution Coding Techniques for Digital
TV", Multidimensional Systems & Signal Processing, 1992, Kluwer
Academic Publishers, Boston, pp. 53-79. .
K. M. Uz et al., "Combined Multiresolution Source Coding &
Modulation . . . ", Signal Processing, 1992, Elsevier Science Pubs.
pp. 283-290..
|
Primary Examiner: Kuntz; Curtis
Assistant Examiner: Vo; Don N.
Attorney, Agent or Firm: deBlasi; Gerard A.
Claims
We claim:
1. Transmitter apparatus comprising,
means for encoding first and second portions of a stream of input
data using first and second redundancy codes, respectively, to
generate multi-level-coded words each of which has a value and
includes at least one data element from each encoded portion, said
first code having a minimum Hamming distance that is greater than a
minimum Hamming distance of said second code,
means for selecting signal points of a predetermined signal
constellation as a function of the values of said multi-level-coded
words, and
means for transmitting a signal representing the selected signal
points over a fading communication channel,
said constellation and codes being such that, in the transmission
of said signal, a probability of error for said first portion is
less than a probability of error for said second portion.
2. The transmitter apparatus of claim 1 wherein said stream of
input data represents information and wherein said first and second
portions of said stream of input data respectively represent more
and less important aspects of said information.
3. The transmitter apparatus of claim 1 wherein the signal points
of said constellation are of equal amplitude.
4. The invention of claim 3 wherein said signal points are
non-uniformly spaced in phase.
5. The transmitter apparatus of claim 1 wherein said constellation
and said selecting means are such as to modulate said
multi-level-coded words using differential phase shift keying.
6. The transmitter apparatus of claim 1 wherein said first code has
a degree of built-in time-diversity which is greater than a degree
of built-in time-diversity of said second code.
7. Transmitter apparatus for communicating a plurality of streams
of data over a channel characterized by Rayleigh fading, said
apparatus comprising
means for encoding said plurality of streams using respective
associated redundancy codes to generate multi-level-coded words,
each of which having a value,
means for selecting signal points of a predetermined signal
constellation as a function of the values of said multi-level-coded
words, and
means for transmitting a signal representing the selected signal
points over said communication channel, said channel being such
that, for an i.sup.th one of said streams,
where
SNR is a signal-to-noise ratio of said channel,
d.sub.Hi is a minimum Hamming distance for the code which encodes
said i.sup.th stream of data,
P.sub.e (i) is a probability of error, upon decoding, for said
i.sup.th stream of data, and
.gamma..sub.i is a proportionality constant for said i.sup.th
stream of data which is a function of said codes and said
constellation,
said codes and said constellation being chosen such that the value
of P.sub.e (i) decreases for decreasing values of i.
8. The transmitter apparatus of claim 7 wherein each
proportionality constant .gamma..sub.i is a ratio of a) an average
number of nearest neighbors for an i.sup.th class of data to b) a
product distance for that class.
9. The transmitter apparatus of claim 7 wherein the signal points
of said constellation are of equal amplitude.
10. The invention of claim 9 wherein said signal points are
nonuniformly spaced in phase.
11. Communications apparatus comprising,
means for encoding first and second portions of a stream of input
data using first and second redundancy codes, respectively, to
generate multi-level-coded words each of which has a value and
includes at least one data element from each encoded portion, said
first code having a minimum Hamming distance that is greater than a
minimum Hamming distance of said second code,
means for selecting signal points of a predetermined signal
constellation as a function of the values of said multi-level-coded
words,
means for transmitting a signal representing the selected signal
points over a communication channel having multiplicative Rayleigh
noise as the predominant noise phenomenon,
means for receiving said signal from said channel, and
means for recovering said stream of input data from the received
signal,
said constellation and codes being such that, in the transmission
of said signal, a probability of error for said first portion is
less than a probability of error for said second portion.
12. The apparatus of claim 11 wherein said first code has a degree
of built-in time-diversity which is greater than a degree of
built-in time-diversity of said second code.
13. The apparatus of claim 12 wherein said stream of input data
represents information and wherein said first and second portions
of said stream of input data respectively represent more and less
important aspects of said information.
14. The apparatus of claim 13 wherein the signal points of said
constellation are of equal amplitude.
15. The invention of claim 14 wherein said signal points are
nonuniformly spaced in phase.
16. The apparatus of claim 13 wherein said constellation and said
selecting means are such as to modulate said multi-level-coded
words using differential phase shift keying.
17. Communications apparatus for communicating a plurality of
streams of data over a channel characterized where multiplicative
Rayleigh noise is a predominant noise phenomenon, said apparatus
comprising
means for encoding said plurality of streams using respective
associated redundancy codes to generate multi-level-coded words,
each of which having a value,
means for selecting signal points of a predetermined signal
constellation as a function of the values of said multi-level-coded
words,
means for transmitting a signal representing the selected signal
points over said communication channel, said channel being such
that, for an i.sup.th one of said streams,
where
SNR is a signal-to-noise ratio of said channel,
d.sub.Hi is a minimum Hamming distance of the code which encodes
said i.sup.th stream of data,
P.sub.e (i) is a probability of error, upon decoding, for said
i.sup.th stream of data, and
.gamma..sub.i is a proportionality constant for said i.sup.th
stream of data which is a function of said codes and said
constellation,
said codes and said constellation being chosen such that the value
of P.sub.e (i) decreases for decreasing values of i,
means for receiving said signal from said channel, and
means for recovering said plurality of streams of data from the
received signal.
18. The transmitter apparatus of claim 17 wherein the
proportionality constant .gamma..sub.i is a ratio of a) an average
number of nearest neighbors for an i.sup.th class of data to b) a
product distance for that class.
19. A method comprising the steps of
encoding first and second portions of a stream of input data using
first and second redundancy codes, respectively, to generate
multi-level-coded words each of which has a value and includes at
least one data element from each encoded portion, said first code
having a minimum Hamming distance that is greater than a minimum
Hamming distance of said second code,
selecting signal points of a predetermined signal constellation as
a function of the values of said multi-level-coded words, and
transmitting a signal representing the selected signal points over
a fading communication channel,
said constellation and codes being such that, in the transmission
of said signal, a probability of error for said first portion is
less than a probability of error for said second portion.
20. The method of claim 19 wherein said stream of input data
represents information and wherein said first and second portions
of said stream of input data respectively represent more and less
important aspects of said information.
21. The method of claim 19 wherein the signal points of said
constellation are of equal amplitude.
22. The method of claim 19 wherein said constellation and said
selecting means are such as to modulate said multi-level-coded
words using differential phase shift keying.
23. The method of claim 19 wherein said first code has a degree of
built-in time-diversity which is greater than a degree of built-in
time-diversity of said second code.
24. A method for communicating a plurality of streams of data over
a channel characterized by Rayleigh fading, said method comprising
the steps of
encoding said plurality of streams using respective associated
redundancy codes to generate multi-level-coded words, each of which
has a value,
selecting signal points of a predetermined signal constellation as
a function of the values of said multi-level-coded words,
transmitting a signal representing the selected signal points over
said communication channel, said channel being such that, for an
i.sup.th one of said streams,
where
SNR is a signal-to-noise ratio of said channel,
d.sub.Hi is a minimum Hamming distance of the code which encodes
said i.sup.th stream of data,
P.sub.e (i) is a probability of error, upon decoding, for said
i.sup.th stream of data, and
.gamma..sub.i is a proportionality constant for said i.sup.th
stream of data which is a function of said constellation,
said codes and said constellation being chosen such that the value
of P.sub.e (i) decreases for decreasing values of i,
receiving said signal from said channel, and
recovering said plurality of streams of data from the received
signal.
25. The method of claim 24 wherein each proportionality constant
.gamma..sub.i is a ratio of a) an average number of nearest
neighbors for an i.sup.th class of data to b) a product distance
for that class.
26. A method for processing a signal generated by the steps of
encoding first and second portions of a stream of input data using
first and second redundancy codes, respectively, to generate
multi-level-coded words each of which has a value and includes at
least one data element from each encoded portion, said first code
having a minimum Hamming distance that is greater than a minimum
Hamming distance of said second code,
selecting signal points of a predetermined signal constellation as
a function of the values of said multi-level-coded words, and
transmitting a signal representing the selected signal points over
a communication channel having multiplicative Rayleigh noise as a
predominant noise phenomenon,
said constellation and codes being such that, in the transmission
of said signal, a probability of error for said first portion is
less than a probability of error for said second portion,
said method comprising the steps of
receiving said signal from said channel, and
recovering said stream of input data from the received signal.
27. The method of claim 26 wherein said first code has a degree of
built-in time-diversity which is greater than a degree of built-in
time-diversity of said second code.
28. The method of claim 27 wherein said stream of input data
represents information and wherein said first and second portions
of said stream of input data respectively represent more and less
important aspects of said information.
29. The method of claim 28 wherein the signal points of said
constellation are of equal amplitude.
30. The method of claim 29 wherein said signal points are
non-uniformly spaced in phase.
31. The method of claim 28 wherein said constellation and said
selecting step are such as to modulate said multi-level-coded words
using differential phase shift keying.
Description
BACKGROUND OF THE INVENTION
The present invention relates to the transmission of information in
digital form over fading channels.
The increasing prominence of wireless
telecommunications--particularly in the realm of digital cellular
mobile radio--has given rise to the demand for improvements in the
bandwidth efficiency of such systems. To this end, efficient coded
modulation schemes, such as the built-in time-diversity technique
disclosed in U.S. Pat. No. 5,029,185, issued to L. F. Wei on Jul.
2, 1991 and entitled "Coded Modulation for Mobile Radio," have been
developed. Increased bandwidth efficiency is also achieved in these
systems via the use of low-bit-rate speech coders, such as the
so-called code-excited linear predictive (CELP) coders, which
operate in the range of about 4 to 8 kilobits per second
(kbps).
The low-bit-rate coders represent speech information in such a way
that certain aspects of the coded information is of significantly
greater importance than other aspects in terms of being able to
recover intelligible speech at the receiver. In CELP coders, for
example, that so-called "important information" may comprise a) the
linear predictive coding (LPC) parameters, b) the pitch, and c) a
bit of information which indicates whether the speech was voiced or
unvoiced. It is thus desirable that the transmission scheme be able
to communicate the "important information" with a high degree of
reliability, even at the expense--if channel conditions make it
necessary--of the other, "less important" information. Such
transmission schemes are referred to herein generically as schemes
which provide "unequal error protection." And it should also be
noted at this point that, in general, there can be any desired
number of classes of information, of varying importance, rather
than being limited to, for example, two classes.
Transmission schemes which provide unequal error protection are, in
fact, known in the prior art. Such known technology is exemplified
by, for example, in Carl-Erik Sundberg, "Optimum Weighted PCM for
Speech Signals," IEEE Transactions on Communications, Vol. COM-26,
No. 6, June 1978, pp. 872-881; C.-E. W. Sundberg et al.,
"Logarithmic PCM weighted QAM transmission over Gaussian and
Rayleigh fading channels," IEE Proceedings, Vol. 134, Pt. F, No. 6,
October 1987, pp. 557-570; and in the commonly assigned co-pending
patent applications of V. B. Lawrence et al., Ser. No. 07/611,225
filed Nov. 7, 1990 (now U.S. Pat. No. 5,164,963, issued Nov. 17,
1992) and entitled "Coding for Digital Transmission," and of L. F.
Wei, Ser. No. 07/611,200 filed Nov. 7, 1990 (now U.S. Pat. No.
5,105,442, issued Apr. 14, 1992) and entitled "Coded Modulation
with Unequal Error Protection." Wireless telecommunications of the
type that the present invention is concerned with are typically
carried out over so-called fading channels, by which is meant
so-called Rayleigh or near-Rayleigh channels, where multiplicative
Rayleigh noise is the predominant noise phenomenon. However, the
prior art (for coded modulation) has generally addressed the
unequal error protection problem in the context of transmission of
the information over, for example, voiceband telephone channels and
HDTV channels, where additive white Gaussian noise is the
predominant noise phenomenon, and those schemes will not perform
effectively if used for the fading environment. Moreover, although
aforementioned coded modulation schemes as disclosed in the Wei
patent application are, in fact, directed to fading channel
applications, they provide equal error protection for the
transmitted data rather than the unequal error protection that is
so highly desirable for the aforementioned coded speech
applications. It can also be noted that schemes which provide
unequal error protection in conjunction with binary and quaternary
phase shift keyed signals are known in the prior art. See
"Rate-compatible punctured convolutional codes for digital mobile
radio," by J. Hagenauer, N. Seshadri and C.-E. W. Sundberg in IEEE
Transactions on Communications, Vol. 37, No. 7, July 1990. However,
these schemes are limited to a maximum of two bits per symbol,
irrespective of the signal-to-noise ratio (SNR) of the channel and
are thus bandwidth-inefficient. Moreover, even when achieving two
bits per symbol, these schemes are power-inefficient.
There thus remains in the art the need for effective, bandwidth-
and power-efficient transmission schemes which can provide unequal
error protection in fading channel environments.
SUMMARY OF THE INVENTION
The present invention meets that need. In particular, in accordance
with the principles of the invention, the information is coded
using a multi-level channel code, by which is meant that a) each
class of information is redundancy coded using a different,
respective channel code and that b) the resulting multi-level-coded
words select for transmission signal points of a predetermined
signal constellation. In preferred embodiments, the minimum Hamming
distance (defined below) for the code used for any particular class
of information is greater than the minimum Hamming distance for the
code used for any less important class of information. The error
probability for channels characterized by Rayleigh fading assuming
adequate interleaving (as described below), and coherent or
differential coherent detection, at high SNR is, to a first, and
typically adequate, approximation, proportional to the reciprocal
of the signal-to-noise ratio (SNR) raised to the power of the
minimum Hamming distance (assuming the use of, for example, a
maximum likelihood decoding strategy). That is, for the i.sup.th
class of data, class i,
where d.sub.Hi is the minimum Hamming distance, .sub..gamma.i is a
proportionality constant and P.sub.e (i) is the probability of
error upon decoding. Different levels of error protection are thus
provided for the different classes of data.
As is explained in detail hereinbelow, the proportionality constant
.sub..gamma.i depends primarily on the ratio of a) the average
number of nearest neighbors for the i.sup.th class of data to b)
the product distance for that class. These parameters are
determined by a) the channel codes and b) the signal constellation
design, the latter including, for example, the constellation
geometry, the labelling of the signal points and the manner in
which the outputs of the channel codes map into the labels. Thus,
in accordance with a feature of the invention, attainment of
particular desired error probabilities for the various different
data classes can be facilitated by appropriate joint selection of
channel codes and signal constellation design.
The prior art does disclose the use of multi-level codes in a
fading channel environment, but only in the context of providing
equal error protection. Exemplary is N. Seshadri and C.-E. W.
Sundberg, "Multi-level codes with large time-diversity for the
Rayleigh fading channel," Conference on Information Sciences and
Systems, Princeton, N.J., pp. 853-857, March 1990. Additionally,
co-pending, commonly assigned U.S. patent application Ser. No.
07/785,723 filed Oct. 31, 1991 discloses the use of multi-level
codes to provide unequal error protection, but not in the context
of fading channels.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 is a block diagram of a transmitter embodying the principles
of the invention;
FIG. 2 is a block diagram of a receiver for signals transmitted by
the transmitter of FIG. 1;
FIG. 3 depicts a signal constellation useful in explaining the
principles of the invention;
FIG. 4 is a block diagram of a multi-level encoder used in the
transmitter of FIG. 1; and
FIGS. 5-7 depict signal constellations that can illustratively be
used by the transmitter of FIG. 1.
DETAILED DESCRIPTION
Before proceeding with a description of the illustrative
embodiments, it should be noted that various of the digital
signaling concepts described herein are all well known in, for
example, the digital radio and voiceband data transmission (modem)
arts and thus need not be described in detail herein. These include
such concepts as multidimensional signaling using 2N-dimensional
channel symbol constellations, where N is some integer, trellis
coding; scrambling; passband shaping; equalization; Viterbi, or
maximum-likelihood, decoding; etc. These concepts are described in
such U.S. patents as U.S. Pat. No. 3,810,021, issued May 7, 1974 to
I. Kalet et al; U.S. Pat. No. 4,015,222, issued Mar. 29, 1977 to J.
Werner; U.S. Pat. No. 4,170,764, issued Oct. 9, 1979 to J. Salz et
al; U.S. Pat. No. 4,247,940, issued Jan. 27, 1981 to K. H. Mueller
et al; U.S. Pat. No. 4,304,962, issued Dec. 8, 1981 to R. D.
Fracassi et al; U.S. Pat. No. 4,457,004, issued Jun. 26, 1984 to A.
Gersho et al; U.S. Pat. No. 4,489,418, issued Dec. 18, 1984 to J.
E. Mazo; U.S. Pat. No. 4,520,490, issued May 28, 1985 to L. Wei;
and U.S. Pat. No. 4,597,090, issued Jun. 24, 1986 to G. D. Forney,
Jr.--all of which are hereby incorporated by reference.
It may also be noted before proceeding that various signal leads
shown in the FIGS. may carry analog signals, serial bits or
parallel bits, as will be clear from the context.
Turning now to FIG. 1, which illustratively depicts a digital
cellular mobile radio terminal such as might be installed in an
automobile, speech signal source 101 generates an analog speech
signal representing speech information or "intelligence," which is
passed on to speech encoder 104, illustratively a CELP coder of the
type described above. The latter generates a digital signal
comprised of a stream of data, or data elements, in which at least
one subset of the data elements represents a portion of the
information, or intelligence, that is more important than the
portion of the information, or intelligence, represented by the
rest of the data elements. Illustratively, each data element is a
data bit, with an average K=k.sub.1 +k.sub.2 +k.sub.3 information
bits being generated for each of a succession of M symbol
intervals. The symbol intervals are comprised of N signaling
intervals, where 2N is the number of dimensions of the
constellation (as described below). The signaling intervals have
duration of T seconds and, accordingly, the symbol intervals each
have a duration of NT seconds. The embodiments explicitly disclosed
herein happen to use two-dimensional constellations, i.e., N=1. For
those embodiments, then, the signaling intervals and symbol
intervals are the same.
Of the aforementioned K information bits, the bits within the
stream of k.sub.1 bits per M symbol intervals, appearing on lead
105, are more important than the k.sub.2 bits per M symbol
intervals, appearing on lead 106, and in turn these bits are more
important than the k.sub.3 bits per M symbol intervals appearing on
lead 107. The bits on these three leads are referred to herein as
the class 1, and class 2 and class 3 bits, respectively.
The bits on leads 105-107 are independently scrambled in scramblers
110-112, which respectively output on leads 115-117 the same number
of bits per M symbol intervals as appear on leads 105-107,
respectively. (In particular specific embodiments, scrambling may
not be required.) Scrambling is customarily carried out on a serial
bit stream. Thus although not explicitly shown in FIG. 1,
scramblers 110-112 may be assumed to perform a parallel-to-serial
conversion on their respective input bits prior to scrambling and a
serial-to-parallel conversion at their outputs. The signal is then
channel encoded and mapped. In particular, the bits on leads
115-117 are extended to multi-level coder 120. As described in
detail hereinbelow, the latter illustratively includes three
channel encoders which respectively receive the bits on leads
115-117. These encoders generate, for each block of M symbol
intervals, a block of M multibit (illustratively 3-bit),
multi-level-coded, words. M is greater than (k.sub.1 +k.sub.2
+k.sub.3)/3 so that the multi-level encoder is a redundancy coder,
i.e., more bits are output than are input. The multi-level code
implemented by encoder 120 to generate the multi-level-coded words
lead 121 has so-called built-in time-diversity. Those bits comprise
a multi-level-coded word and their values jointly select, or
identify, a particular channel symbol of a predetermined
constellation of channel symbols (such as the constellation of FIG.
5 as described in detail hereinbelow). Complex plane coordinates of
the identified channel symbols are output by constellation mapper
131, illustratively realized as a lookup table or as a
straightforward combination of logic elements. The complex channel
symbols are interleaved in standard fashion by an interleaver 141
in order to be able to take advantage of the built-in
time-diversity of the multi-level code. Since such interleaving is
standard, it suffices for present purposes simply to note that the
function of the interleaver is to provide adequate time-separation
between signal points which comprise a coded block to ensure that
fading events associated with those signal points are, in general,
independent. The output of interleaver 141 is applied to modulator
151 and the resultant analog signal is then broadcast via antenna
152 over a free space communication channel to a remote digital
cellular mobile radio cell site.
In order to understand the theoretical underpinnings of the
invention, it will be useful at this point to digress to a
consideration of FIG. 3. The latter depicts a standard
two-dimensional data transmission constellation of the general type
conventionally used in digital cellular mobile radio. In this
standard scheme--conventionally referred to as differential phase
shift keyed (DPSK) modulation--data words each comprised of two
information bits are each mapped into one of four possible
two-dimensional channel symbols. The phase angle of each signal
point (measured from the positive X axis) indicates a change that
the phase of the transmitted signal must undergo in order to
transmit the bit pattern associated with that particular signal
point. More particularly, so-called .pi./4-shifted DPSK, in which
the entire constellation is rotated by 45 degrees in successive
signaling intervals, can be used. (Non-differential (coherent) PSK,
where each signal point represents the associated bit pattern
directly, could alternatively be used in appropriate applications.)
Each channel symbol has an in-phase, or I, coordinate on the
horizontal axis and has a quadrature-phase, or Q, coordinate on the
vertical axis. The signal points have equal amplitude--lying on a
circle of radius 1--so that, on each axis, the channel symbol
coordinates are ##EQU1## Thus the distance between each symbol and
each of the symbols that are nearest to it is the same for all
symbols--that distance being .sqroot.2. As a result of this uniform
spacing, essentially the same amount of noise immunity is provided
for both information bits.
We now define some useful terminology: "Hamming distance," "minimum
Hamming distance," "number of nearest neighbors," and "product
distance." In particular, the "Hamming distance" between any two
distinct sequences of signal points selected from the constellation
is the number of positions within the two sequences at which the
signal points differ. The "minimum Hamming distance" is the minimum
over all such Hamming distances, i.e., taking into account all
possible pairs of sequences. Since we are assuming at this point an
uncoded transmission scheme, all possible sequences of signal
points are allowed. This being so, the minimum Hamming distance for
an uncoded transmission scheme is "1". A code which has so-called
built-in time-diversity has a minimum Hamming distance which is
greater than "1", the measure of that time-diversity being, in
fact, the minimum Hamming distance. The "product distance" is the
product of all non-zero squared Euclidean distances between the
corresponding signal points of the sequences that are at minimum
Hamming distance from each other--known as the "nearest neighbor
sequences." For the present case, the product distance is "2". The
"number of nearest neighbors" is the average number of sequences
that are at the minimum Hamming distance to any transmitted
sequence with a product distance of 2 and, in this case, the
"number of nearest neighbors" is "2".
As is well known, it is possible to provide improved noise immunity
without sacrificing bandwidth efficiency (information bits per
signaling interval) using a coded modulation approach in which an
"expanded" two-dimensional constellation having more than (in this
example) four symbols is used in conjunction with a trellis or
other channel code. For example, the above-cited U.S. Pat. No.
5,029,185 discloses the use of expanded PSK constellations in
combination with trellis and block codes to provide enhanced noise
immunity of more than 10 dB over the uncoded case of FIG. 3 while
providing approximately two bits per signaling interval.
In the above-cited '185 patent as, indeed, in the case of FIG. 3
hereof, the same amount of noise immunity is provided for all
information bits. Thus, as noted above, there remains in the art
the need for effective, bandwidth- and power-efficient transmission
schemes which can provide unequal error protection in fading
channel environments--a need that is met by the present
invention.
In particular, in accordance with the principles of the invention,
the information is coded using a multi-level channel code, by which
is meant that a) each class of information is channel coded using a
different, respective channel code and that b) the resulting coded
outputs select for transmission signal points of a predetermined
signal constellation.
To this end, and referring to FIG. 4, there is shown an
illustrative embodiment of multi-level--illustratively
three-level--channel coder 120. As noted earlier, the three classes
of data are received on leads 115-117, from most-to
least-important. The bit streams for these three classes are
denoted i.sub.1, i.sub.2 and i.sub.3 and are applied to respective
channel encoders 40i, i=1, 2, 3, i.e., encoders 401, 402 and 403,
which respectively implement redundancy codes C.sub.i, i=1, 2, 3,
i.e., codes C.sub.1, C.sub.2 and C.sub.3. The output bit streams
from the three channel encoders--which are buffered in buffers 411,
412 and 413, as described below--are denoted b.sub.1, b.sub.2 and
b.sub.3 and appear on leads 122-124, respectively. The constituent
elements of the output bit streams can be represented as follows,
in which the superscripts denote time:
The multi-level encoder output is
The index b.sup.j then constitutes an address applied to
constellation mapper 131 to select a particular signal point of an
illustrative 8-PSK constellation which is shown in FIG. 5. Note, in
particular, that each of the eight signal points of the
constellation has an associated label--shown in both binary and, in
parentheses, decimal form--which is used as the address. Various
ways of assigning the signal point labels to achieve certain
overall error probabilities for particular codes and particular
constellations are discussed hereinbelow.
The codes respectively implemented by encoders 40i, i=1, 2, 3, are
codes which are characterized by the parameter set (M, k.sub.i and
d.sub.Hi), i=1, 2, 3. Here, M, introduced above, is the block
length of the code; k.sub.i, introduced above, is the number of
information bits required to be applied to encoder 40i to generate
the output block; and d.sub.Hi is the minimum Hamming distance
(defined above) of code C.sub.i. The three codes are illustratively
as follows: Code C.sub.1 is a (4,1,4) binary repetition code
consisting of codewords 0000 and 1111; code C.sub.2 is a (4,3,2)
binary parity check code with even parity; and code C.sub.3 is a
(4,4,1) code, which means that, in this example, no redundancy is
added. That is, class 3 is not coded at all. Since M=4, and since
each signal point is a two-dimensional signal point, the overall
coded modulation scheme is 8-dimensional (8D). The class 1
bits--which are the most important--are encoded by code C.sub.1 ;
the class 2 bits--which are the second-most important--are encoded
by code C.sub.2 ; the class 3 bits--which are the third-most
important--are encoded by code C.sub.3. In order to provide
three-bit addresses to constellation mapper 131 on an ongoing,
regular basis, buffers 411, 412 and 413, each of length M=4, are
provided, as already noted, to buffer the outputs of encoders 401,
402 and 403. It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =8.
That is, 8 information bits are transmitted for each block of M=4
symbol intervals, yielding a bit rate of 2 bits per signaling
interval. Note that 1/8=12.5% of the data is in class 1;3/8=37.5%
of the data is in class 2; and 4/8=50.0% of the data is in class
3.
In order to advantageously use the minimum Hamming distance
separation, i.e., the built-in time-diversity of a code, it is
necessary that symbols within any one block of M signal points be
subject to independent fading. In practice this is achieved by way
of the interleaving provided by interleaver 141 as described
above.
We consider, now, specifically the error probability for each of
the data classes in this example. We first note that the typical
cellular mobile radio channel is a Rayleigh fading channel. The
probability of error for such channels is, to a first, and
typically adequate, approximation, proportional to the reciprocal
of the signal-to-noise ratio (SNR) raised to the power of the
minimum Hamming distance (assuming the use of, for example, a
maximum likelihood decoding strategy). That is, for the i.sup.th
class of data ##EQU2## where d.sub.Hi is the minimum Hamming
distance
P.sub.e (i) is the probability of error upon decoding and
.gamma..sub.i is a proportionality constant.
(Hereinafter, for convenience, we will use "P.sub.e (i)=" rather
than "P.sub.e (i).apprxeq.".) Therefore, since the minimum Hamming
distance for class 1 is "4," which is greater than that for any
less important class of data for which the minimum Hamming distance
is "2", the bit error probability for the former is, in accordance
with the invention, better (i.e., lower) than that for the latter,
assuming some minimum SNR and ignoring, in the first instance, the
contributions of the proportionality constants .gamma..sub.i.
Of course, it is readily seen that the proportionality constants
.gamma..sub.i do also make a contribution to P.sub.e (i). Each
.gamma..sub.i, in particular, is proportional to is the ratio of a)
the average number of nearest neighbors for the i.sup.th class of
data to b) the so-called product distance for that class.
(Hereinafter, for convenience, we will use ".gamma..sub.i =" rather
than ".gamma..sub.i .apprxeq.".) These parameters are determined by
codes chosen, as well as the signal constellation design, which
includes, for example, the constellation geometry, the labelling of
the signal points and the manner in which the outputs of the
channel codes map into the labels. Thus, in accordance with a
feature of the invention, attainment of particular desired error
probabilities for the various different data classes can be
facilitated by appropriate joint selection of channel codes and
signal constellation design. In virtually all instances of
practical interest, the code selection and constellation design
will be such that the values of the .gamma..sub.i will not change
the result that P.sub.e (i)<P.sub.e (2)<P.sub.e (3) . . . for
d.sub.Hi >d.sub.H2 >d.sub.H3 . . . .
The product distance for the class 1 data is 0.587.sup.4 =0.119,
which can be verified by noting that the minimum Hamming distance
of code C.sub.1 is "4" and that the squared Euclidean distance
between nearest neighbors of the signal constellation which differ
in the bit that is addressed by the output of code C.sub.1 --bit
b.sub.1 --is 0.587. The number of nearest neighbors for this code
is 8 since, corresponding to any transmitted multi-level-coded
words, there are 8 other multi-level-coded words which are at a
Hamming distance of 4 with a product distance of 0.119. Thus,
For class 2 data, the product distance is 2.sup.2 =4, which can be
verified by noting the minimum Hamming distance of code C.sub.2 is
"2" and that the squared Euclidean distance between nearest
neighbors of the signal constellation which differ in the bit that
is addressed by the output of this code is 2.0. The number of
nearest neighbors for this code is 6 since for each
multi-level-coded word (assuming i.sub.1 has been decoded
correctly), there are 6 multi-level-coded words that are at a
Hamming distance of 2 that can result in an error in information
sequence i.sub.2. Thus,
For class 3 data, the product distance is 2.0, which can be
verified by noting the minimum Hamming distance for an uncoded
case--which is what code C.sub.3 is in this example--is "1" since
the squared Euclidean distance between nearest neighbors of the
signal constellation which differ in the bit that is addressed by
the output of this code is 2.0. The number of nearest neighbors for
this code is "1" since there is only one neighbor at squared
Euclidean distance "2.0" (assuming that the bits encoded by codes
C.sub.2 and C.sub.1 have been decoded correctly). Thus,
Overall, then,
so that data classes 1, 2 and 3 have the following error
probabilities:
Note that as desired--at least when the SNR is greater than some
minimum--the greatest level of error protection (lowest error
probability) is provided to class 1; the second-greatest level of
error protection is provided to class 2; and the third-greatest
level of error protection is provided to class 3.
(In this example, as well as all the other examples given herein,
it is assumed that the interleaver provides sufficient separation
in time between the signal points within a block of M signal points
to ensure that fading events associated with those signal points
are, in general, independent.)
It will be immediately apparent, then, that using different
codes--to provide different minimum Hamming distances--and
different constellations--to provide different proportionality
constants--various different sets of levels of protection can be
provided. A few different possibilities--which are, of course,
illustrative and not in any sense exhaustive--will now be
presented. We begin by changing the codes while continuing to use
the constellation and signal point labelling of FIG. 5.
Consider, for example, a 16-D block coded modulation scheme which
uses the following set of codes:
It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =18. That is, 18
information bits are transmitted for each block of M=8 symbol
intervals, yielding a bit rate of 2.25 bits per signaling interval.
Note that 4/18=22.2% of the data is in class 1; 7/18=39.9% of the
data is in class 2; and 7/18=39.9% of the data is in class 3.
Overall, then,
so that data classes 1, 2 and 3 have the following error
probabilities:
It will be readily seen that, in this case, the same level of error
protection is provided to classes 2 and 3, yielding, in effect, a
two-rather than a three-level unequal error protection scheme.
However, as will be seen later, using a different constellation
design--while not affecting the minimum Hamming distance--can
result in a change of the proportionality constants, thereby
providing different levels of error protection for classes 2 and
3.
Now we consider a 32-D block coded modulation scheme which uses the
following set of codes:
It is thus seen that K=k.sub.1 +k.sub.2 +k.sub.3 =41. That is, 41
information bits are transmitted for each block of M=16 symbol
intervals, yielding a bit rate of 2.56 bits per signaling interval.
Note that 11/41=26.8% of the data is in class 1; 15/41=36.6% of the
data is in class 2, and 15/41=36.6% of the data is in class 3.
Overall, then,
so that data classes 1, 2 and 3 have the following error
probabilities:
Note that in this case, the error probabilities are approximately
the same as in the previous example. However, the bits per symbol
are different.
Now we consider a coded modulation scheme affording two, rather
than three, levels of error protection and in which a binary
convolutional code is used for protecting the class 1 data and a
block code is used for protecting the class 2 data. The codes, in
particular, are:
Code C.sub.1, more particularly, is a maximum free distance
(d.sub.free) code for any memory of the code that is desirable and
is of the type described, for example, in J. G. Proakis, Digital
Communications, 2nd Ed., McGraw-Hill, 1989. The two bits output by
code C.sub.1 determine bits b.sub.1 and b.sub.2 and the output from
code C.sub.2 determines b.sub.3. In this case, the total number of
bits transmitted in a block of length L is K=(2L-1), yielding a bit
rate of 2-(1/L) bits per signaling interval. Approximately 50% of
the bits are in each of the classes 1 and 2, for reasonably large
L. For example, if code C.sub.1 is a memory 2 convolutional code,
and L=10, then
Moreover, as is well known, the parameter for convolutional codes
which corresponds to the role of the minimum Hamming distance for
block codes is, in this case, (d.sub.free -2)=3. In general, an
upper bound on the value of time diversity for convolutional codes
used in the manner described here is d.sub.free -2. For memory 2
code, this upper bound is achieved. Overall, then, data classes 1
and 2 have the following error probabilities:
(For this example, in order to achieve the above error
probabilities, and, in particular, the product distances indicated,
the labeling assignment shown in FIG. 5 should be changed. The 000
label is assigned to the same signal point of the constellation.
The other labels, reading counter-clockwise, are then, for this
case, 001, 011, 010, 100, 101, 111 and 110.)
The foregoing examples thus illustrate that by using codes having
various a) minimum Hamming distances (or convolutional code free
distance) and b) block code lengths, one can obtain various levels
of error protection, overall bits per signaling interval, and/or
the fraction of bits allocated to the various classes. As noted
earlier, yet further flexibility is provided by using various
different constellations, thereby changing the proportionality
constants .gamma..sub.i.
FIGS. 6 and 7 show respective 8-point PSK constellations in which
the signal points are non-uniformly spaced and for which, as a
result one can provide a) numbers of nearest neighbors and/or b)
product distances that are different from those obtained for the
constellation of FIG. 5. In this way, different proportionality
constants .gamma..sub.i can, advantageously, be obtained.
Consider the use of these constellations in conjunction with the
first set of codes described above for the 8-dimensional block
code.
In the constellation of FIG. 6, in particular, the squared minimum
Euclidean distance between any two signal points that differ in bit
b.sub.1 --that is the bit that is output by encoder 401--is 2.0.
Hence using this constellation in place of the constellation of
FIG. 5 increases the product distance from 0.119 to 16 for class 1.
However, the product distance for class 2 decrease from 4 to 0.43,
while the product distance for class 3 decrease from 2.0 to 1.0.
The number of nearest neighbors for class 1 decreases from 8 to 1,
while for classes 2 and 3 it remains the same as it was, at 6 and
1, respectively. The proportionality constants thus have the
values
Note, then, that the overall result is to provide even greater
error protection (lower error probability) for class 1 at the
expense of less error protection for classes 2 and 3. Thus, the
minimum SNR at which class 1 data bits are subject to a better
error probability is strictly lower with the constellation of FIG.
6 than with that of FIG. 5.
In the constellation of FIG. 7, in particular, the squared minimum
Euclidean distance between any two signal points that differ in
either of bits b.sub.1 or b.sub.2 --that is the bits that are
output by encoders 401 and 402--is 1.0. Hence using this
constellation in place of the constellation of FIG. 5 increases the
product distance from 0.119 to 1.0 for class 1. However, the
product distance for class 2 decreases from 4.0 to 1.0, while the
product distance for class 3 decreases from 4 to 0.43. The number
of nearest neighbors for class 1 decreases from 8 to 1; for class
2, it remains at 6; and for class 3, it remains the same as it was
at 1. The proportionality constants thus have the values
Here, the overall result is to provide a greater separation, in
terms of level of error protection between classes 2 and 3 than
with either of the other two constellations. Class 1 still has more
protection than when the constellation of FIG. 5 is used, but not
as much as when the constellation of FIG. 6 is used.
It may also be possible to use codes which have the same minimum
Hamming distance, in which case unequal error protection can
nonetheless be obtained by having different values of .gamma..sub.i
via, for example, the use of non-uniform signal constellations such
as those of FIGS. 6 and 7.
We turn, now, to the receiver of FIG. 2.
In particular, the analog cellular mobile radio signal broadcast
from antenna 152 is received by antenna 201 and is thereupon
subjected to conventional front-end processing, which includes at a
minimum, demodulation and A/D conversion. Demodulation can be
carried out by any of the known techniques, such as coherent
demodulation, differentially coherent demodulation, non-coherent
demodulation, etc. The front-end processing may also include such
other processing as equalization, timing recovery, automatic gain
control, etc., as is well known in the art. The output of front-end
processing 211 is applied to de-interleaver 221, which performs the
inverse task of interleaver 141 in the transmitter, thereby
restoring the signal points to their original order. The
de-interleaver output is passed on to multi-level decoder 231,
which performs the task of recovering the information bits that
were encoded by multi-level encoder 120. In the general case, a
maximum-likelihood decoding algorithm is used. In particular, if
the multi-level code is sufficiently simple, an exhaustive
table-lookup approach can be used. For more complex codes, then the
Viterbi algorithm could be used if the constituent codes of the
multi-level code allow for a finite-state decoder realization. If
the number of states of the multi-level code is too great to permit
a practical implementation of a maximum-likelihood decoder, then
multi-stage decoding can be used, this approach being described,
for example, in A. R. Calderbank, "Multilevel codes and multi-stage
decoding," IEEE Transactions on Communications, Vol. 37, pp.
222-229, March 1989. Enhanced multi-stage decoding as described in
N. Seshadri and C.-E. W. Sundberg, "Multi-level codes with large
time-diversity for the Rayleigh fading channel," Conference on
Information Sciences and Systems, Princeton, N.J., pp. 853-857,
March 1990, can also be used. More specifically in that case, if
any of the constituent codes are complex, e.g. Reed-Solomon, block
codes, then any of the known decoding techniques that approximate
the performance of the maximum-likelihood decoder for such a code
can be used to deal with that code within the multi-stage
decoder.
The bits output by multi-level decoder 231 are provided in three
parallel streams--corresponding to the three streams on leads
115-117--to respective descramblers 241-243, which perform the
inverse function to scramblers 110-112 in the transmitter. Speech
decoder 253 then performs the inverse function of speech encoder
104 of the transmitter, yielding a reconstructed speech signal that
is passed on to the telephone network, including, typically, a
cellular mobile radio switching system with which the receiver is
co-located.
A transmitter and a receiver similar to those of FIGS. 1 and 2
would, of course, be provided at the cell site and mobile
(automobile) site, respectively, to support communication in the
other direction of transmission.
The foregoing merely illustrates the principles of the invention.
For example, the various codes and constellations, including their
dimensionalities are all illustrative. Any desired codes and
constellations can be used. With respect to the codes, in
particular, it should be noted that a data stream which is not
actually redundancy coded, as is the case for code C.sub.3 the
first example hereinabove, may nonetheless be said to be coded with
a rate R=1 redundancy code. That is, "no coding" can be
regarded--and, for definitional purposes herein, is regarded--as
being a form of coding. With the respect to the constellations, in
particular, any of various uniform or non-uniform configurations
which have any desired number of signal points may be used
advantageously to provide different proportionality constants.
Moreover, any desired number of levels of error protection can be
supported by using multiple multi-level codes to encode respective
sets of data streams and time-multiplexing the signal points
addressed by the various multi-level codes.
The invention can be used to advantage in conjunction with any type
of source coder (such as image, facsimile) that needs unequal error
protection--not just speech coders.
It will also be appreciated that although the various functional
elements of the transmitter and receiver are depicted as discrete
elements, the functions of those elements will typically be carried
out using appropriately programmed processors, digital signal
processing (DSP) chips, etc.
Thus it will be appreciated that those skilled in the art will be
able to devise numerous arrangements which, although not explicitly
shown or described herein, embodying the principles of the
invention and thus are within its spirit and scope.
* * * * *